Method for determining constraints of a non-geostationary system with respect to another non-geostationary system

ABSTRACT

A method for determining operational constraints for a first constellation of non-geostationary satellites (CONS_I) transmitting towards a terrestrial station (SV) with respect to a second constellation of non-geostationary satellites (CONS_V) linked with the station, the constraints comprising a maximum transmission power of the satellites of the first constellation, the method includes determining triplets of limit values (θ, φ, I/N) of two angles (θ, φ) and of an interference-to-noise ratio (I/N), the angles (θ, φ) defining a position of a satellite (NGSO_I) of the first constellation relative to the station and to a satellite (NGSO_V) of the second constellation and the interference-to-noise ratio being the ratio between interferences (I) transmitted by the first constellation on a link between the station and the satellite of the second constellation and the noise (N) of the link, the determination of the triplets being performed so that a distribution of signal-to-noise and interference ratios (R) aggregated over a time interval is greater than a reference distribution (REF); determining at least the maximum transmission power of at least one satellite of the first constellation from the triplets.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to foreign French patent applicationNo. FR 1908699, filed on Jul. 31, 2019, the disclosure of which isincorporated by reference in its entirety.

FIELD OF THE INVENTION

The invention relates to a method for determining operationalconstraints to be observed for a first constellation ofnon-geostationary satellites transmitting towards a terrestrial stationat a point on the Earth with respect to a second constellation ofnon-geostationary satellites linked with the same terrestrial station.This method also makes it possible to determine the operationalconstraints to be observed for a first terrestrial station linked with afirst constellation of non-geostationary satellites transmitting towardsa satellite belonging to a second constellation of non-geostationarysatellites and linked with a second terrestrial station at a point onthe Earth.

BACKGROUND

The international regulations require the different non-geostationarysystems to be coordinated in order to avoid interfering with oneanother. This coordination is generally reflected by the definition andthe setting up of acceptable levels of interference and by operationalconstraints which can lead to a reduction of capacity of certainsystems.

The need for coordination is a genuine constraint because it demands theprotection of and/or protection from all the types of stations of theother constellations over the service zones of these otherconstellations, if the zones are known, even to protect or be protectedfor all the points on the Earth, without knowing the direction in whichthe terminal that is victim of an interference is aiming.

FIG. 1 represents a diagram of the existing solutions for coordinatingnon-geostationary systems. A satellite NGSO1 of a firstnon-geostationary constellation CONS1 is linked with a terrestrialstation S1 at a point on the Earth. A topocentric angle θ is definedbetween the satellite NGSO1, the terrestrial station S1 and a satelliteNGSO2 of a second non-geostationary constellation CONS2. The satelliteNGSO2 will be able to transmit towards the terrestrial station S1 onlyif the topocentric angle θ is greater than a predetermined angle, forexample equal to 10°.

This condition on the topocentric angle imposes strong constraints onthe interfering constellation CONS2, which are greater than the needs ofthe system suffering the interferences from the constellation CONS2,this system comprising the first constellation CONS1 and the terrestrialstation S1. These constraints are therefore fairly strict andinflexible.

Furthermore, that requires a large number of operational constraints tobe taken into account by the operational module managing the radioresources.

SUMMARY OF THE INVENTION

The invention aims to remedy the abovementioned drawbacks of the priorart, more particularly it aims to propose a method for determiningoperational constraints for a first constellation of non-geostationarysatellites transmitting towards a terrestrial station linked with asecond constellation of non-geostationary satellites. It aims also topropose a method for determining operational constraints for a firstterrestrial station transmitting towards a non-geostationary satelliteof a constellation of non-geostationary satellites linked with a secondterrestrial station. The method according to the invention notably makesit possible to adapt the topocentric angle threshold below which thetransmission from the satellites of the first constellation or from thefirst terrestrial station is prohibited, and thus obtain constraintsthat fit a precise operational situation.

One object of the invention is therefore a method, implemented bycomputer, for determining operational constraints to be observed for afirst constellation of non-geostationary satellites transmitting towardsa terrestrial station at a point on the Earth with respect to a secondconstellation of non-geostationary satellites linked with theterrestrial station, the operational constraints comprising at least amaximum transmission power of the satellites of the first constellation,the method comprising the steps of: determining triplets of limit valuesof two angles and of an interference-to-noise ratio, the two anglesdefining a position of a satellite of the first constellation relativeto an axis formed by the terrestrial station and a satellite of thesecond constellation and the interference-to-noise ratio being the ratiobetween the interferences transmitted by the first constellation on alink between the terrestrial station and the satellite of the secondconstellation and the noise of the link, the determination of thetriplets being performed in such a way that a distribution ofsignal-to-noise and interference ratios aggregated over a time intervalis greater than a reference distribution, the signal-to-noise andinterference ratios being the ratios between a useful signal of the linkand the noise and the interferences;

determining at least the maximum transmission power of at least onesatellite of the first constellation from the triplets of values.

According to embodiments:

the triplets of limit values are determined by the following steps:

1) selecting, for each instant of a time interval, satellites of thefirst constellation and a satellite of the second constellation anddetermining, for each instant of the time interval, a triplet of anglevalues defining a position of the selected satellites of the firstconstellation with respect to an axis formed by the terrestrial stationand the selected satellite of the second constellation and ofsignal-to-noise and interference ratio, the signal-to-noise andinterference ratio being the signal-to-noise and interference ratio ofthe selected satellites of the first constellation with respect to thelink between the terrestrial station and the selected satellite of thesecond constellation;2) determining the instants of the time interval and adjusting thesignal-to-noise and interference ratio value of the triplet of theseinstants in such a way that a distribution of the signal-to-noise andinterference ratios aggregated over the time interval is greater than areference distribution;3) determining triplets of values at the determined instants and asurface equation parameterized by the triplets, the triplets of values(θ, φ, I/N) being the angles (θ, φ) defining the position of a selectedsatellite of the first constellation and I/N being aninterference-to-noise ratio on the link determined by the adjustedsignal-to-noise and interference ratios, the points of this surfaceequation representing the triplets of limit values (θ, φ, I/N).

The selection of the satellites in the step 1) is done so as to minimizea signal-to-noise and interference ratio on a link between theterrestrial station and a satellite of the second constellation.

The method comprises the following steps performed after the step 3):

4) For each instant of the time interval and for a satellite of thesecond constellation linked with the terrestrial station, selectingsatellites of the first constellation that have angle values and aninterference-to-noise ratio on the link between the terrestrial stationand the satellite of the second constellation, such that, for theseangle values, the interference-to-noise ratio is less than or equal tothe interference-to-noise ratio obtained by the surface equation forthese same angle values;5) determining the instants of the time interval and adjusting thesignal-to-noise and interference ratio value of the selected satellitesof the first constellation for these instants so as to minimize thedifference between a distribution of the signal-to-noise andinterference ratios aggregated over the time interval of the selectedsatellites and a reference distribution, the distribution of theaggregate signal-to-noise and interference ratios being greater than thereference distribution;6) determining a second surface equation parameterized by the angle andinterference-to-noise ratio values adjusted from the adjustedsignal-to-noise and interference ratios of the selected satellites atthe instants determined in the step 5), the points of this secondsurface equation representing the triplets of the limit values (θ, φ,I/N).

The method comprises the following steps performed after the step 3):

3′) determining the angle values defining the position of a satellite ofthe first constellation transmitting towards the terrestrial stationlinked with a satellite of the second constellation and theinterference-to-noise ratio of the satellite of the first constellationon the link between the terrestrial station and the satellite of thesecond constellation;3″) comparing the interference-to-noise ratio to theinterference-to-noise ratio determined by the surface equation for theangle values determined in 3′), so that:

if the interference-to-noise ratio is less than or equal to thatdetermined by the surface equation, retaining or increasing thetransmission power of the satellite of the first constellation so thatits interference-to-noise ratio remains lower than that of the surfaceequation;

if the interference-to-noise ratio is greater than that obtained withthe surface equation, reducing the transmission power of the satelliteof the first constellation so that its interference-to-noise ratio isgreater than or equal to that of the surface equation.

The method is implemented for a plurality of assumed positions ofterrestrial stations.

The satellites of the first constellation and the satellite of thesecond constellation selected in the step 1) are those that minimize thevalue of an angle defining the position of the satellites of the firstconstellation relative to the axis formed between the terrestrialstation and a satellite of the second constellation.

Another object of the invention is a method, implemented by computer,for determining operational constraints to be observed for a firstterrestrial station at a point on the Earth, transmitting towards anon-geostationary satellite of a constellation of non-geostationarysatellites linked with a second terrestrial station with respect to thelink between the satellite and the second terrestrial station, theoperational constraints comprising at least a maximum transmission powerof the first terrestrial station, the method comprising the steps of:

determining triplets of limit values (θ, φ, I/N) of two angles and of aninterference-to-noise ratio, the two angles defining a position of thefirst terrestrial station relative to an axis formed by the secondterrestrial station and the non-geostationary satellite and theinterference-to-noise ratio being the ratio between interferencestransmitted by the first terrestrial station on the link between thesecond terrestrial station and the non-geostationary satellite and thenoise of the link, the determination of the triplets being performed insuch a way that a distribution of signal-to-noise and interferenceratios aggregated over a time interval is greater than a referencedistribution, the signal-to-noise and interference ratios being theratios between a useful signal of the link and the noise and theinterferences;

determining at least the maximum transmission power of the firstterrestrial station from the triplets of values.

According to embodiments:

the triplets of limit values (θ, φ, I/N) are determined by the followingsteps:

1) selecting, for each instant of a time interval, first terrestrialstations and a non-geostationary satellite linked with the secondterrestrial station, and determining, for each instant of the timeinterval, a triplet of angle values defining a position of the firstterrestrial stations selected relative to an axis formed by the secondterrestrial station and the non-geostationary satellite and thesignal-to-noise and interference ratio, the signal-to-noise andinterference ratio being the signal-to-noise and interference ratio ofthe first stations selected with respect to the link between the secondterrestrial station and the non-geostationary satellite;2) determining the instants of the time interval and adjusting thesignal-to-noise and interference ratio value of the triplet of theseinstants so that a distribution of the signal-to-noise and interferenceratios aggregated over the time interval is greater than a referencedistribution;3) determining triplets of values (θ, φ, I/N) at the determined instantsand a surface equation parameterized by the triplets (θ, φ, I/N), thetriplets of values being the angles defining the position of the firstterrestrial stations selected relative to the axis formed by the secondterrestrial station and the non-geostationary satellite and I/N being aninterference-to-noise ratio on the link between the second terrestrialstation and the non-geostationary satellite determined by the adjustedsignal-to-noise and interference ratios, the points of this surfaceequation representing the triplets of limit values (θ, φ, I/N).

The selection of the terrestrial stations and of the non-geostationarysatellite in the step 1) is performed so as to minimize asignal-to-noise and interference ratio on a link between the secondterrestrial station and the selected non-geostationary satellite.

The method comprises the following steps performed after the step 3):

4) For each instant of the time interval and for the second terrestrialstation, selecting first terrestrial stations at points on the Earth anda non-geostationary satellite linked with the second terrestrialstation, such that the first terrestrial stations have angle values andan interference-to-noise ratio on the link between the secondterrestrial station and the non-geostationary satellite, and that, forthese angle values, the interference-to-noise ratio is less than orequal to the interference-to-noise ratio obtained by the surfaceequation for these same angle values;5) determining the instants of the time interval and adjusting thesignal-to-noise and interference ratio value of the first terrestrialstations selected for these instants, so as to minimize the differencebetween a distribution of the signal-to-noise and interference ratiosaggregated over the time interval of the first selected stations and areference distribution, the distribution of the aggregatesignal-to-noise and interference ratios being greater than the referencedistribution;6) determining a second surface equation parameterized by the angle andinterference-to-noise ratio values adjusted on the basis of the adjustedsignal-to-noise and interference ratios of the first terrestrialstations selected at the instants determined in the step 5), the pointsof this second surface equation representing the triplets of limitvalues (θ, φ, I/N).

The method comprises the following steps performed after the step 3):

3′) determining the angle values defining the position of a firstterrestrial station transmitting towards a non-geostationary satellitewith the second terrestrial station and the interference-to-noise ratioof the first terrestrial station on the link between the secondterrestrial station and the non-geostationary satellite;3″) comparing the interference-to-noise ratio to theinterference-to-noise ratio determined by the surface equation for theangle values determined in 3′), so that:

if the interference-to-noise ratio is less than or equal to thatdetermined by the surface equation, retaining or increasing thetransmission power of the first terrestrial station so that itsinterference-to-noise ratio remains lower than that of the surfaceequation;

if the interference-to-noise ratio is greater than that obtained withthe surface equation, reducing the transmission power of the firstterrestrial station so that its interference-to-noise ratio is greaterthan or equal to that of the surface equation.

The method is implemented for a plurality of assumed positions of thesecond terrestrial station.

The first terrestrial stations and the non-geostationary satelliteselected in the step 1) are those minimizing an angle value defining theposition of the first terrestrial stations relative to an axis formed bythe second terrestrial station and the selected non-geostationarysatellite.

Another object of the invention is a computer program comprisinginstructions for executing the method for determining triplets of limitvalues (θ, φ, I/N) according to the invention, when the program is runby a processor.

Yet another object of the invention is a processor-readable storagemedium, on which is stored a program comprising instructions forexecuting the method for determining triplets of limit values (θ, φ,I/N) according to the invention; when the program is run by a processor.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features, details and advantages of the invention will emerge onreading the description given with reference to attached figures whichare given by way of example and which represent, respectively:

FIG. 1, already described, a diagram representing the currentconstraints of the constellations of non-geostationary satellites withrespect to another non-geostationary system according to the prior art;

FIG. 2a and

FIG. 2b , two diagrams of the principle of the method according to theinvention for two application cases;

FIG. 3, a diagram of the steps of the method according to a firstembodiment;

FIG. 4, a diagram of the steps of the method according to a secondembodiment;

FIG. 5 and

FIG. 6, two figures representing the principle of the step 2) of themethod according to the invention; and

FIG. 7, a figure representing a surface equation obtained by the methodaccording to the invention.

DETAILED DESCRIPTION

FIG. 2a represents a diagram of the principle of the method according tothe invention in a first application case. This first application caserepresents a downlink. A constellation CONS_V, comprising severalsatellites situated on a non-geostationary orbit and comprising meanscapable of communicating with one or more terrestrial stations,comprises a non-geostationary satellite NGSO_V linked with a terrestrialstation SV situated at a point on the Earth. The satellite NGSO_Vtherefore sends and/or receives signals C that are called useful to theterrestrial station SV.

Another constellation CONS_I comprises a non-geostationary satelliteNGSO_I transmitting signals I to the terrestrial station SV. Thesesignals can interfere with the link between the terrestrial station SVand the victim satellite NGSO_V and constitute a source of interferencefor this link. The constellation CONS_V and the satellite NGSO_Vsuffering these interferences are denoted victim constellation andvictim satellite hereinafter in the description.

The topocentric angle θ is defined as the angle formed between thesatellite NGSO_V and the satellite NGSO_I from the terrestrial stationSV, and the elevation angle φ is defined as the angle formed between theplane TAN tangential to the ground at the terrestrial station SV and theaxis formed by the terrestrial station SV and the satellite NGSO_I.These two angles θ and φ make it possible to define a position of thesatellite NGSO_I relative to the satellite NGSO_V and to the station SV.

The objective of the method is to define the maximum power value of theinterference signal I that the satellite NGSO_I can transmit to thestation SV for a topocentric angle value θ and an elevation angle valueφ that are fixed, by generating an acceptable level of interferenceswith respect to the constellation CONS_V. In other words, the objectiveof the method is to determine a maximum power for each satellite NGSO_Iof the constellation CONS_I by taking account of the possibleinterferences generated with respect to the satellites NGSO_V of anotherconstellation CONS_V situated in its vicinity. For that, triplets oflimit values (θ, φ, R) of a topocentric angle θ, of an elevation angle φand of a signal-to-noise and interference ratio R are determined in sucha way that a distribution of signal-to-noise and interference ratios Raggregated over a time interval is greater than a reference distributionREF.

The signal-to-noise and interference ratio R is the ratio between auseful signal C of the link between the terrestrial station SV and thesatellite NGSO_V of the victim constellation CONS_V and the noise N andthe interferences I transmitted by the interference constellation CONS_Ion this link. In other words, the signal-to-noise and interference ratioR is equal to C/(N+I).

From the signal-to-noise and interference ratio R, it is possible todeduce the maximum transmission power of a satellite NGSO_I of theinterfering constellation CONS_I from the determined triplets of valuesand using theoretical relationships known from the field. Moreparticularly, it is possible to determine, for a given topocentric anglevalue θ and a given elevation angle value φ, the maximum transmissionpower from the signal-to-noise and interference ratio of the triplet ofvalues comprising the given angle values.

FIG. 2b represents a diagram of the principle of the method according tothe invention in a second application case, representing an uplink. Aconstellation CONS_V, comprising several satellites situated on anon-geostationary orbit and comprising means capable of communicatingwith one or more terrestrial stations, comprises a non-geostationarysatellite NGSO_V linked with a terrestrial station SV situated at apoint on the Earth. The satellite NGSO_V therefore sends and/or receivessignals C that are called useful to the terrestrial station SV.

Another terrestrial station SI, called interfering station, is linkedwith a second constellation CONS_I of non-geostationary satellites,notably with a non-geostationary satellite NGSO_I. This otherterrestrial station SI also transmits signals I to the satellite NGSO_Vlinked with the terrestrial station SV. These signals I can interferewith the link between the terrestrial station SV and the satelliteNGSO_V, called victim, and constitute a source of interference for thislink.

In order to identify the position of the interfering terrestrial stationSI, an angle θ formed between the station SV and the interfering stationSI is defined from the victim non-geostationary satellite NGSO_V, and anangle of elevation φ is defined as the angle formed between the planeTAN tangential to the orbit of the victim constellation CONS_V and tothe satellite NGSO_V and the axis formed by the interfering terrestrialstation SI and the satellite NGSO_V. These two angles θ and φ make itpossible to define the position of the station SI relative to thesatellite NGSO_V and to the station SV.

The objective of the method, for this second application case, is todefine the maximum power value of the interfering signal I that thestation SI can transmit to the satellite NGSO_V for an angle value θ andan angle value φ that are fixed, by generating an acceptable level ofinterference with respect to the constellation CONS_V. In other words,the objective of the method is to determine a maximum power for eachterrestrial station SI by taking account of the possible interferencesgenerated with respect to satellite NGSO_V of a constellation CONS_Vlinked with a terrestrial station SV situated in its vicinity. For that,triplets of limit values (θ, φ, R) of the angles θ, φ and of asignal-to-noise and interference ratio R are determined so that adistribution of signal-to-noise and interference ratios R aggregatedover a time interval is greater than a reference distribution REF.

The signal-to-noise and interference ratio R is the ratio between auseful signal C of the link between the terrestrial station SV and thesatellite NGSO_V of the victim constellation CONS_V and the noise N andthe interferences I transmitted by the interfering station SI on thislink. In other words, the signal-to-noise and interference ratio R isequal to C/(N+I).

From the signal-to-noise and interference ratio R, it is possible todeduce the maximum transmission power of the station SI from thetriplets of values determined and using theoretical relationships knownin the field. More particularly, it is possible to determine, for givenangle values θ and φ, the maximum transmission power from thesignal-to-noise and interference ratio of the triplet of valuescomprising the given angle values.

FIG. 3 presents a diagram of the steps of the method according to afirst embodiment. The first application case (FIG. 2a ) is taken for thedescription of FIGS. 3 to 7.

In a first step 201, for each instant of a time interval and for aterrestrial station SV at a point on the Earth, satellites of theinterfering constellation CONS_I and a satellite NGSO_V of the victimconstellation CONS_V are selected according to a selection criterion. Inthe example described, the satellites of the interfering constellationCONS_I and a satellite NGSO_V are selected which minimize thesignal-to-noise and interference ratio R on the link between theterrestrial station SV and the satellite of the victim constellationCONS_V. However, it is also possible to select the satellite NGSO_V ofthe victim constellation that has the highest elevation in thisconstellation with respect to the terrestrial station SV. It is alsopossible to select an interfering satellite CONS_I that has the longesttime of visibility with respect to the terrestrial station SV and/or aparticular satellite of the victim constellation CONS_V.

Then, for these same instants, a triplet of values (θ, φ, R) oftopocentric angle θ, of elevation angle φ and of signal-to-noise andinterference ratio R is determined for these selected satellitesrelative to the terrestrial station SV. The topocentric angle θ is theminimum angle formed by the satellite NGSO_V of the victim constellationCONS_V selected, the terrestrial station SV and the selected satellitesNGSO_I of the interfering constellation CONS_I. The elevation angle φ isthe minimum angle formed between the plane TAN tangential to the groundat the terrestrial station SV and the axis formed between theterrestrial station SV and the selected satellites NGSO_I of theinterfering constellation CONS_I. The signal-to-noise and interferenceratio R is the signal-to-noise and interference ratio of the interferingsatellites NGSO_I of the interfering constellation CONS_I on the linkbetween the terrestrial station SV and the victim satellite NGSO_V ofthe victim constellation CONS_V. This ratio R is determined bysimulation.

Then, in a second step 202, a determination is made as to the instantsof the time interval for which it is possible to adjust thesignal-to-noise and interference ratio value R of the triplet of values(θ, φ, R) of these instants so that a distribution of thesignal-to-noise and interference ratios R aggregated over the timeinterval is greater than the reference distribution REF.

FIG. 5 and FIG. 6 illustrate the step 202 of the method.

FIG. 5 represents the percentage of time % t of the time interval as afunction of the signal-to-noise and interference ratio R=C/(N+I). Thecurve REF represents the reference distribution and the curve N1represents aggregate signal-to-noise and interference ratios of thesatellites of the victim and interfering constellations selected withrespect to the terrestrial station, whereas the curve N2 represents thesame signal-to-noise and interference ratios after the identification ofthe time instants for which the value of the signal-to-noise andinterference ratio is adjusted for the curve N1 to be greater than thereference distribution REF.

FIG. 6 represents the signal-to-noise and interference ratio R as afunction of the different instants t of the time interval. It is thesesignal-to-noise and interference ratios aggregated over the timeinterval (therefore aggregated over all the instants t) which make itpossible to obtain the curve N1 of FIG. 5. The identified time instantsINST are represented in FIG. 6 and their signal-to-noise andinterference ratio value R is modified so as to obtain the curve N2 ofFIG. 5.

To determine these instants t of the time interval from FIGS. 5 and 6,it is assumed that the curve N1 of FIG. 5 follows a probability law asfollows:

P _(N1)(X≥x _(n))=p _(n)  (1)

-   -   in which X represents a random variable of the signal-to-noise        and interference ratio R, x_(n) represents a particular value of        a signal-to-noise and interference ratio, p_(n) represents the        time probability corresponding to the signal-to-noise and        interference ratio value x_(n) and n is an integer less than or        equal to the total number of time instants of the time interval.

It is also assumed that the reference distribution REF follows thefollowing probability law:

P _(REF)(X≥x)=p  (2)

-   -   with p a time probability corresponding to the signal-to-noise        and interference ratio value x and X being a random variable        representing a signal-to-noise and interference ratio.

If the curve N1 becomes less than the reference distribution REF for allprobabilities p, then that means that there is an integer i and m suchthat:

P _(N1)(X≥x _(i))=p _(i) and P _(REF)(X≥x _(m))=p _(i) with x _(i) <x_(m)  (3)

and such that:

P _(N1)(X≥x _(m))=p _(m) with p _(m) <p _(i)  (4)

A law of the curve N1 is then sought to be obtained such that:

P _(N1)(X≥x _(i))=p _(m)  (5)

The first step is to identify the greatest value of i that does notobserve the criterion of the equation (5), which means that, forX=x_(i+1), the criterion will be observed. The value x_(i) is thenmodified to become equal to x_(i+1), that is to say that thesignal-to-noise ratio value x_(i) becomes equal to x_(i+1).

That is applied for all the other values of i that do not observe thecriterion of the equation (5) by working through the i values indescending order.

That makes it possible to identify the values x_(i) of signal-to-noiseand interference ratios to be modified. It is now necessary to identifythe time instants t corresponding to these values x_(i). For that, inFIG. 6, it is possible to identify all the signal-to-noise andinterference ratios that are equal to the identified values x_(i), thenmodify signal-to-noise and interference ratio values of these instantsso that the distribution of the signal-to-noise and interference ratiosR, comprising the modified values, aggregated over the time interval, isgreater than the reference distribution REF.

In the third step 203, triplets of values (θ, φ, I/N) are determined atthe instants determined in the preceding step. The triplets of values(θ, φ, I/N) represent the angles (θ, φ) defining the position of aselected satellite NGSO_I of the first constellation CONS_I and I/Nbeing an interference-to-noise ratio on the link determined by thesignal-to-noise and interference ratios R adjusted in the preceding stepfor the determined instants.

In this step, a surface equation parameterized by the triplets of values(θ, φ, I/N) is also determined. The points of the surface equationrepresent the triplets of limit values (θ, φ, I/N) authorized for thesatellites of the interfering constellation CONS_I with respect to thelink between the terrestrial station SV and the victim satellite NGSO_V.

In an optional fourth step 203′ and an optional fifth step 203″, therewill be a check as to whether a satellite of the interferingconstellation CONS_I transmitting towards the terrestrial station SVtransmits an interference level that is sufficiently low to preserve thelink between the terrestrial station and a non-geostationary satelliteof the victim constellation CONS_V.

For that, in the fourth step 203′, the topocentric angle θ, elevationangle φ and interference-to-noise ratio I/N values are determined forthe satellite of the interfering constellation CONS_I transmitting tothe terrestrial station SV linked with the satellite of the victimconstellation CONS_V.

Then, in the next step 203″, the interference-to-noise ratio I/N iscompared to the interference-to-noise ratio determined by the surfaceequation of the step 203 for the angle values θ and φ determinedpreviously in 203′.

If the interference-to-noise ratio is less than or equal to the ratiodetermined by the surface equation, that means that the interferingsatellite interferes little on the link between the terrestrial stationand the satellite of the victim constellation. It is not thereforenecessary to reduce the transmission power of the interfering satellite.It may even be possible to increase the transmission power of theinterfering satellite, provided that the signal-to-noise andinterference ratio value remains less than the ratio determined by thesurface equation.

If the signal-to-noise and interference ratio is greater than the ratiodetermined by the surface equation, that means that the interferingsatellite interferes with the link between the terrestrial station andthe satellite of the victim constellation. It is therefore necessary toreduce the transmission power of the interfering satellite so that itssignal-to-noise and interference ratio is greater than or equal to thatdetermined by the surface equation. Instead of reducing the transmissionpower of the interfering satellite, it is also possible to use anothersatellite of the interfering constellation CONS_I to lower the level ofinterference.

FIG. 7 represents a surface equation determined in the third step 203 ofthe method. The surface equation EQ_SURF depends on the two angles θ andφ defining the position of a satellite of the interfering constellationrelative to the link between the terrestrial station SV and a satelliteof the victim constellation and on the signal-to-noise and interferenceratio R defined by the ratio between the useful signal of the linkbetween the terrestrial station and the satellite of the victimconstellation and the sum of the noise and of the interferences on thislink coming from the satellite of the interfering constellation. Theangle θ can be a topocentric angle formed between a satellite of theinterfering constellation, the terrestrial station and a satellite ofthe victim constellation, and the angle φ can be an elevation angleformed between the plane tangential to the terrestrial station and theaxis formed between the terrestrial station and the satellite of theinterfering constellation.

The points of this surface equation EQ_SURF defined by a triplet ofvalues (θ, φ, I/N) represent, for given angle values θ and φ, themaximum interference-to-noise ratio I/N and therefore the maximum levelof interference that the satellite of the interfering constellation canhave on the link.

FIG. 4 represents a diagram of the steps of the method according to asecond embodiment. The first 201, second 202 and third 203 steps areidentical to the steps 201, 202 and 203 described with reference to FIG.3.

In this second embodiment, three additional steps 204, 205 and 206 areperformed to adjust the surface equation determined in the third step203 to an operational situation.

There are therefore selected, in the fourth step 204, for each instantof the time interval and for a satellite of the victim constellationlinked with the terrestrial station, the satellites of the interferingconstellation which have topocentric angle θ, elevation angle φ andinterference-to-noise ratio I/N values such that, for these angle valuesθ and φ, the interference-to-noise ratio I/N is less than or equal tothe interference-to-noise ratio determined by the surface equation ofthe step 203 for these same angle values θ and φ.

Then, in the fifth step 205, a determination is made as to instants ofthe time interval for which it is possible to adjust the signal-to-noiseand interference ratio value so that the distribution of thesignal-to-noise and interference ratios aggregated over the timeinterval of the selected satellites of the interfering constellationwith respect to the link between the terrestrial station and thesatellite of the victim constellation is greater than the referencedistribution.

Finally, in the sixth step 206, a second surface equation is determinedthat is parameterized by the angle θ and cp values andinterference-to-noise ratios I/N adjusted from the signal-to-noise andinterference ratios, adjusted in the step 205, of the selectedsatellites at the instants determined in the preceding step. The pointsof this second surface equation represent the triplets of correctedlimit values (θ, φ, I/N). This second surface equation makes it possibleto protect the two non-geostationary systems (that comprising theinterfering constellation and that comprising the victim constellationand the terrestrial station) while relaxing the constraints defined bythe first surface equation and corresponding to the worst interferingconfiguration between the two constellations, while operationally, thesatellites of the two constellations can be in a more favourableconfiguration.

According to another embodiment, the method is performed for a pluralityof terrestrial station assumptions. For that, if the method is performedfor N terrestrial stations linked with a satellite of the victimconstellation CONS_V, the steps 201, 202 and 203 (and possibly the steps203′, 203″, 204, 205 and 206) are repeated N times, each repetitionbeing performed for a station that is different from the previousrepetitions. It will therefore be necessary on each repetition of thestep 1) to redefine the satellites of the interfering constellationCONS_I and the satellite of the victim constellation CONS_V for eachinstant which minimize the signal-to-noise and interference ratio on thelink.

According to one embodiment, the selection of the satellites of the twoconstellations with respect to the terrestrial station is made in such away as to select the worst case, for example by taking the satellite,from among those minimizing the signal-to-noise and interference ratio,that gives the smallest topocentric angle θ.

According to another embodiment, it is also possible to determinetriplets of limit values (θ, φ, R) in which R represents thesignal-to-noise and interference ratio of the satellites of theinterfering constellation on the link between the terrestrial stationand a satellite of the victim constellation. Thus, it is also possibleto determine a third surface equation from these triplets of values (θ,φ, R).

For that, the triplets of values (θ, φ, R) deriving from the instantsdetermined in the step 202 are used to parameterize a third surfaceequation.

However, if the surface equation parameterized by the triplets (θ, φ, R)is used, the interfering satellites exhibiting ratio R values greaterthan those given by the third surface equation for given angle valueswill be sought to be selected.

For example, for the step 204, the satellites of the interferingconstellation are selected such that, for a given topocentric anglevalue θ and for an elevation angle value φ, the signal-to-noise andinterference ratio R is greater than the ratio R determined by the thirdsurface equation for these same angle values.

According to another example, for the step 203″, the signal-to-noise andinterference ratios R are compared with the ratios determined by thethird surface equation for topocentric and elevation angle valuesdetermined in the step 203′, and the transmission power of thesatellites of the interfering constellation is reduced if the ratio R isless than that determined by the third surface equation.

Nevertheless, the use of the ratio I/N is prioritized, because the ratioI/N is independent of the radio frequency characteristics specific tothe link between the terrestrial station and the satellite of the victimconstellation.

The figures have been described for the first application case. It isalso possible to apply the method for the second application case,namely for an uplink, in which it is a terrestrial station SI whichemits interfering signals I to the link between the terrestrial stationSV and a satellite of the victim constellation. That corresponds to thesituation presented in FIG. 2 b.

In this application case, in the step 201, for each instant of a timeinterval, first terrestrial stations SI at points on the earth,different from the point of the terrestrial station SV, and anon-geostationary satellite of a non-geostationary constellation linkedwith the terrestrial station SV, which minimize a signal-to-noise andinterference ratio R on the link between the terrestrial station SV andthe selected non-geostationary satellite, are selected. There are alsodetermined, for each instant of the time interval, a triplet (θ, φ, R)of angle values (θ, φ) defining a position of the first terrestrialstations SI selected relative to an axis formed by the terrestrialstation SV and the non-geostationary satellite and signal-to-noise andinterference ratio R. The ratios R being the signal-to-noise andinterference ratios of the first stations selected with respect to thelink between the terrestrial station and the non-geostationarysatellite.

In the second step 202, the instants of the time interval are determinedand, for these instants, the signal-to-noise and interference ratiovalue of the triplet (θ, φ, R) of these instants is adjusted so that adistribution of the signal-to-noise and interference ratios aggregatedover the time interval is greater than a reference distribution (REF).

Then, in the step 203, triplets of values (θ, φ, I/N) at the determinedinstants and a surface equation parameterized by the triplets (θ, φ,I/N) are determined. The triplets of values (θ, φ, I/N) are the angles(θ, φ) defining the position of the first terrestrial stations selectedrelative to the axis formed by the second terrestrial station SV and thenon-geostationary satellite NGSO_V and the interference-to-noise ratioI/N on the link between the terrestrial station SV and thenon-geostationary satellite determined by the adjusted signal-to-noiseand interference ratios (R). The points of this surface equationrepresent the triplets of limit values (θ, φ, I/N).

In the case where the aim is to adapt to an operational situation, thesteps described with reference to FIG. 4 are as follows for thisapplication case:

In the step 204, for each instant of the time interval and for thesecond terrestrial station SV, first terrestrial stations at points onthe Earth and a non-geostationary satellite linked with the terrestrialstation SV are selected, such that the first terrestrial stations haveangle values (θ, φ) and an interference-to-noise ratio (I/N) on the linkbetween the terrestrial station SV and the non-geostationary satelliteof the victim constellation, and that, for these angle values, theinterference-to-noise ratio is less than or equal to theinterference-to-noise ratio obtained by the surface equation for thesesame angle values.

Then, in the step 205, the instants of the time interval are determinedand signal-to-noise and interference ratio value (R) of the firstselected terrestrial station for these instants are adjusted, so as tominimize the difference between a distribution of the signal-to-noiseand interference ratios aggregated over the time interval of the firstselected stations and a reference distribution (REF), the distributionof the aggregate signal-to-noise and interference ratios being greaterthan reference distribution.

Finally, in the step 206, a second surface equation is determined thatis parameterized by the angle and interference-to-noise ratio valuesadjusted from the adjusted signal-to-noise and interference ratios ofthe first terrestrial stations selected at the instants determined inthe step 205. The points of this second surface equation represent thetriplets of limit values (θ, φ, I/N).

For the case of FIG. 3, in the step 203′, the angle values (θ, φ)defining the position of a first terrestrial station transmitting towarda non-geostationary satellite linked with the terrestrial station SV andthe interference-to-noise ratio (I/N) of the first terrestrial stationon the link between the terrestrial station and the non-geostationarysatellite are determined.

Then, in the step 203″, the interference-to-noise ratio is compared tothe interference-to-noise ratio determined by the surface equation forthe angle values determined in the step 203′, so as to:

-   -   if the interference-to-noise ratio is less than or equal to that        determined by the surface equation, retain or increase the        transmission power of the first terrestrial station so that its        interference-to-noise ratio remains less than that of the        surface equation;    -   if the interference-to-noise ratio is greater than that obtained        with the surface equation, reduce the transmission power of the        first terrestrial station so that its interference-to-noise        ratio is greater than or equal to that of the surface equation.

As for the first application case, the method can be implemented for aplurality of assumed positions of the terrestrial station SV.

Likewise, the first terrestrial stations and the non-geostationarysatellite selected in the step 201 can be those that minimize an anglevalue, for example 0, defining the position of the first terrestrialstations relative to an axis formed by the second terrestrial stationand the selected non-geostationary satellite.

The method according to the invention has been described in the contextof two non-geostationary constellations. However, the method is notlimited to that, it can also be used in a more general context involvinga non-geostationary constellation and a geostationary constellation.That can for example be in the case where a geostationary constellation(satellite of the constellation or terrestrial station linked with thegeostationary constellation) transmits interfering signals on a linkbetween a terrestrial station on the Earth and a non-geostationaryconstellation. That can also be in the case where a non-geostationaryconstellation (satellite of the constellation or terrestrial stationlinked with the non-geostationary constellation) transmits interferingsignals on a link with a terrestrial station on the Earth and ageostationary constellation.

The invention can be implemented as a computer program comprisinginstructions for the execution thereof. The computer program can bestored on a processor-readable storage medium. The medium can beelectronic, magnetic, optical or electromagnetic.

In particular, the invention can be implemented by a device comprising aprocessor and a memory. The processor can be a generic processor, aspecific processor, an application-specific integrated circuit (knownalso by the acronym ASIC) or a field-programmable gate array (also knownby the acronym FPGA).

The device can use one or more dedicated electronic circuits or ageneral-purpose circuit. The technique of the invention can be producedon a reprogrammable computation machine (a processor or amicrocontroller for example) executing a program comprising a sequenceof instructions, or on a dedicated computation machine (for example aset of logic gates like an FPGA or an ASIC, or any other hardwaremodule).

According to one embodiment, the device comprises at least onecomputer-readable storage medium (RAM, ROM, EEPROM, flash memory oranother memory technology, CD-ROM, DVD or another optical disk medium,magnetic cassette, magnetic tape, computer-readable permanent storagedisk) coded with a computer program (that is to say several executableinstructions) which, when it is run on a processor or severalprocessors, performs the functions of the embodiments of the inventiondescribed previously.

As an example of hardware architecture suitable for implementing theinvention, a device according to the invention can comprise acommunication bus to which there are linked a central processing unit ormicroprocessor (CPU), a read-only memory (ROM) that can comprise theprograms necessary to the implementation of the invention; arandom-access memory or cache memory (RAM) comprising registers suitablefor storing variables and parameters created and modified during theexecution of the abovementioned programs; and a communication or I/O(input/output) interface suitable for transmitting and receiving data.

The reference to a computer program which, when it is run, performs anyone of the functions described previously, is not limited to anapplication program running on a single host computer. On the contrary,the terms computer program and software are used here in a general senseto refer to any type of computing code (for example, applicationsoftware, firmware, microcode, or any other form of computerinstruction) which can be used to program one or more processors toimplement aspects of the techniques described here. The computing meansor resources can notably be distributed (“cloud computing”), possiblyaccording to pair-to-pair technologies. The software code can beexecuted on any appropriate processor (for example, a microprocessor) orprocessor core or a set of processors, whether provided in a singlecomputation device or distributed between several computation devices(for example as possibly accessible in the environment of the device).The executable code of each program allowing the programmable device toimplement the processes according to the invention can be stored, forexample, in the hard disk or in read-only memory. Generally, the programor programs will be able to be loaded into one of the storage means ofthe device before being executed. The central processing unit cancontrol and direct the execution of the instructions or portions ofsoftware code of the program or programs according to the invention,instructions which are stored in the hard disk or in the read-onlymemory or else in the other abovementioned storage elements.

1. A method, implemented by computer, for determining operationalconstraints to be observed for a first constellation ofnon-geostationary satellites (CONS_I) transmitting towards a terrestrialstation (SV) at a point on the Earth with respect to a secondconstellation of non-geostationary satellites (CONS_V) linked with theterrestrial station, the operational constraints comprising at least amaximum transmission power of the satellites of the first constellation,the method comprising the steps of: determining triplets of limit values(θ, φ, I/N) of two angles (θ, φ) and of an interference-to-noise ratio,the two angles (θ, φ) defining a position of a satellite (NGSO_I) of thefirst constellation (CONS_I) relative to an axis formed by theterrestrial station (SV) and a satellite (NGSO_V) of the secondconstellation (CONS_V) and the interference-to-noise ratio (I/N) beingthe ratio between the interferences (I) transmitted by the firstconstellation on a link between the terrestrial station (SV) and thesatellite (NGSO_V) of the second constellation (CONS_V) and the noise(N) of the link, the determination of the triplets being performed insuch a way that a distribution of signal-to-noise and interferenceratios (R) aggregated over a time interval is greater than a referencedistribution (REF), the signal-to-noise and interference ratios (R)being the ratios between a useful signal (C) of the link and the noise(N) and the interferences (I); determining at least the maximumtransmission power of at least one satellite of the first constellationfrom the triplets of values.
 2. The method, implemented by computer, fordetermining operational constraints according to claim 1, wherein thetriplets of limit values (θ, φ, I/N) are determined by the followingsteps: 1) selecting, for each instant of a time interval, satellites ofthe first constellation and a satellite of the second constellation anddetermining, for each instant of the time interval, a triplet (θ, φ, R)of angle values (θ, φ) defining a position of the selected satellites ofthe first constellation (CONS_I) with respect to an axis formed by theterrestrial station (SV) and the selected satellite of the secondconstellation (CONS_V) and of signal-to-noise and interference ratio(R), the signal-to-noise and interference ratio being thesignal-to-noise and interference ratio of the selected satellites of thefirst constellation with respect to the link between the terrestrialstation and the selected satellite of the second constellation; 2)determining the instants of the time interval and adjusting thesignal-to-noise and interference ratio value of the triplet (θ, φ, R) ofthese instants in such a way that a distribution of the signal-to-noiseand interference ratios aggregated over the time interval is greaterthan a reference distribution (REF); 3) determining triplets of values(θ, φ, I/N) at the determined instants and a surface equationparameterized by the triplets (θ, φ, I/N), the triplets of values (θ, φ,I/N) being the angles (θ, φ) defining the position of a selectedsatellite of the first constellation (CONS_I) and I/N being aninterference-to-noise ratio on the link determined by the adjustedsignal-to-noise and interference ratios (R), the points of this surfaceequation representing the triplets of limit values (θ, φ, I/N).
 3. Themethod, implemented by computer, for determining operational constraintsaccording to claim 2, wherein the selection of the satellites in thestep 1) is done in such a way as to minimize a signal-to-noise andinterference ratio (R) on a link between the terrestrial station and asatellite of the second constellation.
 4. The method, implemented bycomputer, for determining operational constraints according to claim 2,comprising the following steps performed after the step 3): 4) for eachinstant of the time interval and for a satellite of the secondconstellation linked with the terrestrial station, selecting satellitesof the first constellation that have angle values (θ, φ) and aninterference-to-noise ratio (I/N) on the link between the terrestrialstation (SV) and the satellite of the second constellation (NGSO_V),such that, for these angle values, the interference-to-noise ratio isless than or equal to the interference-to-noise ratio obtained by thesurface equation for these same angle values; 5) determining theinstants of the time interval and adjusting the signal-to-noise andinterference ratio value (R) of the selected satellites of the firstconstellation for these instants so as to minimize the differencebetween a distribution of the signal-to-noise and interference ratiosaggregated over the time interval of the selected satellites and areference distribution (REF), the distribution of the aggregatesignal-to-noise and interference ratios being greater than the referencedistribution; 6) determining a second surface equation parameterized bythe angle and interference-to-noise ratio values adjusted on the basisof the adjusted signal-to-noise and interference ratios of thesatellites selected at the instants determined in the step 5), thepoints of this second surface equation representing the triplets oflimit values (θ, φ, I/N).
 5. The method, implemented by computer, fordetermining operational constraints according to claim 2, wherein themethod comprises the following steps performed after the step 3): 3′)determining the angle values (θ, φ) defining the position of a satelliteof the first constellation transmitting towards the terrestrial stationlinked with a satellite of the second constellation and theinterference-to-noise ratio (I/N) of the satellite of the firstconstellation on the link between the terrestrial station and thesatellite of the second constellation; 3″) comparing theinterference-to-noise ratio to the interference-to-noise ratiodetermined by the surface equation for the angle values determined in3′), so that: if the interference-to-noise ratio is less than or equalto that determined by the surface equation, retaining or increasing thetransmission power of the satellite of the first constellation so thatits interference-to-noise ratio remains lower than that of the surfaceequation; if the interference-to-noise ratio is greater than thatobtained with the surface equation, reducing the transmission power ofthe satellite of the first constellation so that itsinterference-to-noise ratio is greater than or equal to that of thesurface equation.
 6. The method, implemented by computer, fordetermining operational constraints according to claim 1, wherein themethod is implemented for a plurality of assumed positions ofterrestrial stations.
 7. The method, implemented by computer, fordetermining operational constraints according to claim 2, wherein thesatellites of the first constellation and the satellite of the secondconstellation selected in the step 1) are those minimizing the value ofan angle (θ) defining the position of the satellites of the firstconstellation relative to the axis formed between the terrestrialstation and a satellite of the second constellation.
 8. A computerprogram comprising instructions for executing the method for determiningtriplets of limit values (θ, φ, I/N) according to claim 1, when thisprogram is run by a processor.
 9. A processor-readable storage medium,on which is stored a program comprising instructions for executing themethod for determining triplets of limit values (θ, φ, I/N) according toclaim 1, when the program is run by a processor.